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Abstract: nuclear energy is clean energy technology as it produces zero greenhouse emissions. Most of the nuclear reactor products are from (n, y) reactions. This are free neutrons with kinetic energy and has large effective cross-section. Our objective was examined the solution of partial differential equation for the case in which the medium is unbound, calculated neutron age and thermal energy for C and Be. The stationary equation of the transfer of neutrons with simplifying assumption lead to the function S which describes the source of neutrons, the required quantity u(x,τ) is concentration of neutrons per unit time, reaching the age τ; consequently, u is the density of deceleration. The solution was found by introducing the Fourier map U(ξ,τ) of the density of deceleration U(x,τ). Taking into account the behavior of density of deceleration at infinity, we obtained u(ξ,τ)=(2π)^(-ξ) e^(-ξ^2 τ). When neutrons reach a specific velocity, they cease to lose energy and their motion can be described using classical theory of diffusion. If the medium is infinite, we introduced Fourier images for ρ and q; expressed through the value of the functionq(z). The calculated neutron age for graphite and beryllium were found to be 12 and 9 respectively. In order to simplify the calculation, a continuous loss of energy for slowing down neutrons was assumed in state of actual discontinuous energy loss.
